code: def test_ard_separate_batch(self):
      x1 = torch.tensor(
          [
              [[4, 2, 1], [3, 1, 5]],
              [[3, 2, 3], [6, 1, 7]],
          ],
          dtype=torch.float,
      )
      x2 = torch.tensor([[[4, 2, 1], [6, 0, 0]]], dtype=torch.float)
      lengthscales = torch.tensor(
          [[[1, 2, 1]], [[2, 1, 0.5]]], dtype=torch.float
      )
  
      kernel = CategoricalKernel(
          batch_shape=torch.Size([2]), ard_num_dims=3
      )
      kernel.initialize(lengthscale=lengthscales)
      kernel.eval()
  
      sc_dists = x1.unsqueeze(-2) != x2.unsqueeze(-3)
      sc_dists = sc_dists / lengthscales.unsqueeze(-2)
      actual = torch.exp(-sc_dists.mean(-1))
      res = kernel(x1, x2).to_dense()
      self.assertAllClose(res, actual)
  
      # diag
      res = kernel(x1, x2).diagonal()
      actual = torch.diagonal(actual, dim1=-1, dim2=-2)
      self.assertAllClose(res, actual)
  
      # batch_dims
      actual = torch.exp(-sc_dists).transpose(-1, -3)
      res = kernel(x1, x2, last_dim_is_batch=True).to_dense()
      self.assertAllClose(res, actual)
  
      # batch_dims + diag
      res = kernel(x1, x2, last_dim_is_batch=True).diagonal()
      self.assertAllClose(res, torch.diagonal(actual, dim1=-1, dim2=-2))
  
file_path: botorch/test/models/kernels/test_categorical.py
imports: import torch
  from botorch.models.kernels.categorical import CategoricalKernel
  from botorch.utils.testing import BotorchTestCase
  from gpytorch.test.base_kernel_test_case import BaseKernelTestCase
label_desc: Use image node_id 11 for calling the TestCategoricalKernel obj's underlying member method code with example usage: obj.test_ard_separate_batch() without return types